Fermions and Goldstone bosons in an asymptotically safe model

Abstract

We consider a model in which Goldstone bosons, described by a SU(N) chiral nonlinear sigma model, are coupled to an N-plet of colored fermions by means of a Yukawa interaction. We study the one-loop renormalization group flow and show that the non-Gaussian UV fixed point, which is present in the purely bosonic model, is lost because of fermion loop effects unless N is sufficiently large. We then add four-fermion contact interactions to the lagrangian and show that in this case there exist several non-Gaussian fixed points. The strength of the contact interactions, predicted by the requirement that the theory flows towards a fixed point in the UV, is compared to the current experimental bounds. This toy model could provide an important building block of an asymptotically safe model of the weak interactions.

7 pages, 3 figures, 1 table

References in corpus (3)

• Fixed Points of Nonlinear Sigma Models in d>2
• Asymptotic safety and the gauged SU(N) nonlinear sigma-model
• The electroweak S and T parameters from a fixed point condition

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